Quiz 2

Question 1

Y increases as X increases by?

Answer 1

Slope B

Question 2

Simple linear regression model in words

Answer 2

response = predictor + error

Question 3

What is a signal

Answer 3

Predictor

Question 4

What is noise

Answer 4

Error

Question 5

Formal statistical model:

Answer 5

response = intercept(p) + slope(p) + error “Where p = predictor variable)

Question 6

Descripe linear model when pages is the response variable and words is the predictor

Answer 6

pages = words + error or pages = wordsp + wordsp1 + error

Question 7

Multiple linear regression model

Answer 7

response = predictor 1 + predictor 2 + error

Question 8

Simple linear regression is:

Answer 8

Linear regression with one continuous response variable Y and ONE continuous predictor variable X

Question 9

Multiple linear regression is:

Answer 9

Linear regression with one continuous response variable Y, and MORE THAN ONE continuous predictor.

Question 10

What are the basic assumptions of linear regression

Answer 10

Linear, normally distributed residual with homogeneous variances

Question 11

How does B1 quantify different things between simple and multiple regression

Answer 11

The effects of X1 on Y controlls for effect of X2. Isolates the influence of x1 independent of x2 by estimating b1 holding x2 constant.
Does not allow X2 to interfere when assessing the effect of X1

Question 12

Explain what B1 is in multiple regression model

Answer 12

For every additional X1 (predictor), the number of Y (response) increases by b1, holding the number of X2 constant.

Question 13

Main difference between b1 in linear regression and multiple regression

Answer 13

b1 in linear is regression slope while in regression b1 and b2 are partial regression slopes

Question 14

What is the 2nd complication in multiple linear regression?

Answer 14

Multiple predictors can interact in their effect on the response variable.

Question 15

What is the regression model for interaction? Multiplicative model

Answer 15

response = b1 + b2 + (b3xb2) + error

Question 16

What is the third complication in multiple regression models?

Answer 16

Predictor variables can themselves be corelated

Question 17

What are the assumptions of multiple regression models?

Answer 17

1. Linear relationship between predictor and response variable
2. Equal variance of residuals around regression line
3. normally distributed residual
4. Predictors should not be strongly correlated (ie. no collinearity)

Question 18

How do you detect collinearity?

Answer 18

1. Think about which predictor variables are likely to be collinear before building model
2. Plot predictor variables against each other
3. Calculate the TOLERANCE associated with each predictor.

Question 19

Tolerance

Answer 19

Lower tolerance is bad.
Tolerance < 0.1 is really bad

Question 20

VIR

Answer 20

Variance inflation factor
VIF = 1/tolerance
Higher VIF is bad
VIF >10 is really bad.

Question 21

Method 1 of writing multiple linear regression

Answer 21

Question 22

Method 2 of writing multiple linear regression

Answer 22

Question 23

Types of linear models

Answer 23

Simple
Y = B0 + b1x1 + error
Multiple linear
Y = B0 + B1X1 + B2X2 + error
(More than one continuous predictor variable)
Anova model
Y = B0 + B1X1a + B2X1b + error
(One or more categorical predictor variables that have more than one level [eg. a and b])
Ancova model
Y = B0 +B1X1a + B2X1b +B3X2 + error
(One or more categorical predictor variables that have more than one level AND one or more continuous predictor variables)

Question 24

Linear statistical model with one categorical predictor variable

Answer 24

Yij = u +B1xaij +B2xbij + B3xcij + errorij
Where:
j represents a single observation from single organisms and i represents the level of the predictor
u = Mean of all observations across all levels of all factors
B1 = difference between the mean of ‘a’ (level) and ‘u’ (mean)
B2 = difference between the mean of ‘b’ (level) and ‘u’ (mean)
B2 = difference between the mean of ‘c’ (level) and ‘u’ (mean)

Question 25

What is the sum of all the squared deviation in analysis of variance (SS)(ANOVA)

Answer 25

Eij(Yij - Yj)2 Where Yij = One observation I within group j Yj = mean of all observations in group j

Question 26

DFresidual = ?

Answer 26

n-k where n = total number of observations (true replicates) k = number of levels within the predictor variable (number of groups or factor levels)

Question 27

MS =?

Answer 27

MS = SS / df Average deviation of the data from the group means

Question 28

Write an anova table

Answer 28

Source of var | SS | df | MS | F-value groups | SS | df | SS/df | MSgroups / MSresidual (signal/noise) residuals | SS | df | SS/df | total | SS | df |

Question 29

What is an observational study

Answer 29

Cannot isolate casual drivers from effect of potentially confounding variables. (confounder is a variable that influences both the dependent variable and independent variable)

Question 30

What is an experimental study

Answer 30

Can potentially isolate casual drivers from the effect of confounding variables.

Question 31

Lurking variables examples

Answer 31

Lurking variables can make experiments useless and their influence can only be neutralized with good experimental design. Z X /-->\ Y Z can influence Y through X Z Can directly influence Y The key to strength of experiments is that they allow us to explicitly ISOLATE the effect of X on Y without the lurking variable Z interfering with the experiment.

Question 32

Ways to neutralize lurking variables

Answer 32

1. Replication 2. Randomized design 3. Blocking

Question 33

What are the benefits of replication?

Answer 33

Any casual relationship between variables may be caused by lurking variables we are unaware of. This is also called the sampling effect and small samples are more vulnerable thus we increase replication to minimize interaction from lurking variables. Essential to notice we must replicate the correct thing and avoid pseudoreplication as it increases the F-ratio, which decreases the p-value, which increases the chance we incorrectly reject the null hypothesis.

Question 34

What are the benefits of randomization?

Answer 34

Reducing bias: Randomization helps to reduce the impact of selection bias and confounding variables, which can affect the validity and generalizability of study results. Improving statistical power: Randomization helps to increase the statistical power of a study, which refers to the ability of a study to detect a true effect if it exists.

Question 35

What are the benefits of blocking?